Internal problem ID [3545]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 814.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.047 (sec). Leaf size: 193
dsolve(diff(y(x),x)^2-(1+4*y(x))*diff(y(x),x)+(1+4*y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -{\frac {1}{4}} \\ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-{\mathrm e}^{-2 x} c_{1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}}-{\mathrm e}^{-2 x} c_{1}-2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-{\mathrm e}^{-2 x} c_{1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}}-{\mathrm e}^{-2 x} c_{1}-2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-{\mathrm e}^{-2 x} c_{1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}}+{\mathrm e}^{-2 x} c_{1}+2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-{\mathrm e}^{-2 x} c_{1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}}+{\mathrm e}^{-2 x} c_{1}+2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 67
DSolve[(y'[x])^2-(1+4 y[x])y'[x]+(1+4 y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{x-4 c_1} \left (e^x+2 e^{2 c_1}\right ) \\ y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right ) \\ y(x)\to -\frac {1}{4} \\ y(x)\to 0 \\ \end{align*}